Question

se ( x+y)2-(x-y)2=-20 determine valor numérico de x y

Answer 1

Note que:

$(x+y)^2=x^2+2xy+y^2$

$(x-y)^2=x^2-2xy+y^2$

Assim:

$(x+y)^2-(x-y)^2=x^2+2xy+y^2-(x^2-2xy+y^2)$

$(x+y)^2-(x-y)^2=x^2+2xy+y^2-x^2+2xy-y^2$

$(x+y)^2-(x-y)^2=x^2-x^2+y^2-y^2+2xy+2xy$

$(x+y)^2-(x-y)^2=4xy$

Como $(x+y)^2-(x-y)^2=-20$, segue que:

$4xy=-20~\longrightarrow~xy=\dfrac{-20}{4}~\longrightarrow~\boxed{xy=-5}$